This invention relates to a phase type computer hologram and an optical instrument suitably usable in an optical system such as an optical interconnection system, a lens surface shape measuring system or an illumination optical system, for example.
A process for producing a hologram by use of a computer is called xe2x80x9ccomputer hologramxe2x80x9d. In an earlier stage, it is directed to reproduction of a virtual three-dimensional object. Currently, however, because of its ability of deforming a wavefront of light as desired, it is applied to various optical systems such as an optical interconnection system, a lens surface shape measuring system and an illumination system, for example.
In the computer hologram, amplitudes or phases of incident light rays at different positions on a hologram are changed so that a desired deformation is produced in the wavefront of the incident light, and a desired image is produced through propagation of the deformed wavefront. As an example of a method of causing wavefront deformation, there is a coding method called a xe2x80x9cbinary hologramxe2x80x9d wherein a complex amplitude of a deformed wavefront such as described above is approximated on the basis of a transmission factor distribution of binary levels of black and white. Because a complex amplitude distribution can be reproduced and the process is relatively simple, this method is used widely at present. However, because it is an amplitude type hologram, it involves inconveniences such as a low diffraction efficiency and production of a ghost image due to higher-order diffraction light.
On the other hand, there is a kind of phase type hologram, called a xe2x80x9cKinoformxe2x80x9d wherein the phase of incident light is changed. It is known that, if an idealistic Kinoform is produced, the diffraction efficiency thereof becomes equal to 100%. Such Kinoform may be used as a phase type computer hologram.
A phase type computer hologram can be produced by a method wherein an original with a pattern having a multiple-value density distribution, determined by calculation, is produced by use of an intermediate-tone plotter, and wherein the pattern of the original is transferred onto a dry plate in reduced magnification, the dray plate being thereafter bleached to produce a phase type hologram. Recently, however, a method in which a shape is directly produced upon a substrate surface by cutting, and a method in which a binary optics is produced while approximating a Kinoform-like shape with a step-like shape by use of a photolithographic process, are used widely. Particularly, because a very fine structure can be produced at a good precision, the latter method is used in many cases for production of surface relief type diffraction optical elements, in general, not only for production of hologram.
In phase type diffraction optical elements such as a Kinoform described above, the phase of light impinging on the element is changed by an amount determined by a phase function applied. While such phase function can be expressed by a function xcfx86(x, y) of the position (x, y) upon the element, since the phase term of light has a period of 2xcfx80, a change of xcfx86(x, y) (mod2xcfx80) will be sufficient in practice. Such a phase change may be applied by forming an appropriate curved surface upon a substrate to produce a suitable optical path difference. However, if xcfx86(x, y) is a continuous function, then xcfx86(x, y) (mod2xcfx80) will change continuously within a certain zone, while, at a position as folded by xe2x80x9cmodxe2x80x9d, it takes discontinuous points having a difference 2xcfx80.
Considering this in terms of the surface of a substrate, while the shape changes smoothly within a certain zone, there is produced, at the discontinuous points, a surface step (level difference) of optical path length xcex corresponding to the phase 2xcfx80. As regards the shape which is continuous only in a certain zone, it becomes very difficult to form such shape if the width of the zone is small. In consideration of it, there is a method in which the shape in that zone is approximated by a step-like shape.
The concept described above basically applies to a phase type computer hologram. However, usually, no curved surface is formed on a substrate in accordance with a phase function-applied. Rather, in many cases, from the size and resolution of an image desired, the size of cells as a whole as well as the size of each cell necessary for a phase type computer hologram are calculated and, on the basis of which, phase values for the cells are optimized. Here, xe2x80x9ccellsxe2x80x9d refer to small areas as divided by what is called a xe2x80x9cmeshxe2x80x9d.
Here, the phases of the cells may be set continuously, in a range from 0-2xcfx80. In order to provide these phase values on the basis of the surface shape, the depth direction has to be controlled continuously. If this is done through an etching process, the control has to be made separately with respect to individual cells and, therefore, the process for continuous depth control is difficult to accomplish. In consideration of it, the phase values of the cells may be set to 2xcfx80j/N (where N is a natural number and 0xe2x89xa6j less than Nxe2x88x921) and a solution for phase distribution may be obtained. On the basis of it, an etching process may be repeated N times, at the maximum, by which a phase type computer hologram may be produced.
However, as regards a binary optics element such as shown in FIG. 7, for example, having a sectional shape corresponding to a phase type computer hologram where N=4, particularly when an element equivalent to a lens is considered, although the phase function usually changes monotonously, there is no such monotonous change present in the case of a phase type computer hologram which requires complicated wavefront deformation as compared with the lens. Therefore, when considered one-dimensionally, there may be a case wherein the phase value of successive three cells once skips by more than xcfx80, at the position of a cell 3 and then turns back. In terms of surface shape, this corresponds to a protrusion or a recess having a height (depth) of xcex/2 or more. Particularly where the size of the cells is small, it is very difficult to produce such shape with a good precision,
It is accordingly an object of the present invention to provide a phase type computer hologram having a good shape precision.
In accordance with an aspect of the present invention, there is provided a phase type computer hologram, characterized by a plurality of cells for applying a predetermined phase to different portions of a wavefront of light, wherein no phase skip larger than it is present in the cells.
In accordance with another aspect of the present invention, there is provided a method of producing a phase type computer hologram, comprising the steps of: determining phases for a plurality of cells, respectively; smoothening a distribution of the phases of the cells, by shifting the phase of at least one of the cells by 2xcfx80; and forming, on a substrate, the cells whose phase distribution is smoothened in said smoothening step.
The smoothening step may include shifting the phase of at least one cell by 2xcfx80 so that a least square error related to the cell phase is reduced.
The smoothening step may further include (i) a process for separating the cells into plural groups and detecting, with respect to each groups, a least square error related to the cell phase, and (ii) a process for shifting, by 2xcfx80, the phase of said at least one cell in a cell group or groups where the detected least square error is larger than a threshold value, to thereby reduce the least square error related to the cell phase.
The phase type computer hologram may be a hologram having a phase distribution.
The phase type computer hologram may be a hologram having a phase distribution and an amplitude distribution.
In accordance with a further aspect of the present invention, there is provided a system including a hologram produced in accordance with a method as described above.
In accordance with a yet further aspect of the present invention, there is provided an exposure apparatus having an illumination system including a hologram produced in accordance with a method as described above.
In accordance with a still further aspect of the present invention, there is provided a device manufacturing method, comprising the steps of: illuminating a device pattern by use of an illumination system including a hologram produced in accordance with a method as recited above, so that a substrate is exposed with the device pattern; and developing the exposed substrate.
A phase type computer hologram according to the present invention may be a hologram of a type having a phase structure only, or it may be a hologram of a type having both a phase structure and an amplitude structure. Some preferred embodiments of the present invention to be described below, show holograms of both of these types, wherein a phase skip of cells is kept not greater than xcfx80.
In a phase type computer hologram according to one preferred form of the present invention, at least one of cells has a level difference (step) having been changed by an amount corresponding to a multiple, by an integer, of a wavelength (design wavelength) of light to be used, in respect to the optical path length defined by the step
In a phase type computer hologram according to another preferred form of the present invention, one or more cells in a certain region have a level. difference (step) having been changed by an amount corresponding to a multiple, by an integer, of a wavelength (design wavelength) of light to be used, in respect to the optical path length defined by the step, so that an average square error of the steps of the cells in that region or of the cells of the whole is reduced.
In a phase type computer hologram according to a further preferred form of the present invention, at least one of cells of the hologram has a height having been changed by an amount corresponding to a multiple, by an integer, of a wavelength (design wavelength) of light to be used, in respect to the optical path length defined by passage through that cell, such that a level difference (step) with an adjacent cell is reduced.
In a phase type computer hologram according to a yet further preferred form of the present invention, at least one of cells in a certain region has a height having been set so that the optical path length changes by an amount corresponding to a multiple, by an integer, of a wavelength (design wavelength) of light to be used, so that an average square error of the steps of the cells in that region or of the cells of the whole is minimized.
In a phase type hologram producing method according to one preferred form of the present invention, evaluation is made to phase skip among cells at least in a certain region of the hologram and, if there is a phase skip larger than a predetermined value, the phase value of a cell or cells in that region is increased or decreased by 2xcfx80, by which the phase skip in that region is minimized.
These and other objects, features and advantages of the present invention will become more apparent upon a consideration of the following description of the preferred embodiments of the present invention taken in conjunction with the accompanying drawings.